Influence of pump-phase fluctuations on entanglement generation using a correlated spontaneous-emission laser

In this paper, we study the effect of phase fluctuations of the pump field upon the entanglement generation in a two-photon correlated emission laser (CEL). We consider initial vacuum and coherent state for the two-cavity modes. In both cases, we find reduction in the entanglement due to the phase fluctuations. However, our results indicate that entanglement generation is highly sensitive to phase fluctuations when we have initial coherent state in the two modes.

Figure 1

Schematic for the entanglement amplifier. A three-level atomic system in a cascade configuration. The transition between levels $\mid a⟩$-$\mid b⟩$ and $\mid b⟩$-$\mid c⟩$ at frequencies ${\nu }_1$ and ${\nu }_2$ are resonant with the cavity. The transition $\mid a⟩$-$\mid c⟩$ is dipole forbidden and can be induced by a strong magnetic field.

Figure 2

Time development of (a) $⟨\widehat{N}⟩$ and (b) $(\mathrm{\Delta }\widehat{u}{)}^2+(\mathrm{\Delta }\widehat{v}{)}^2$ for the initial vacuum states for the two modes (in terms of normalized interaction time $gt$) with $\Omega =400\mathrm{kHz}$, $\Gamma =20\mathrm{kHz}$, ${\kappa }_1={\kappa }_2=3.85\mathrm{kHz}$, $r_a=22\mathrm{kHz}$, $g=g_1=g_2=43\mathrm{kHz}$ (parameters are chosen such that they correspond to the micromaser experiments [20]) for $D∕\Gamma =0,0.01$, and 0.02.

Figure 3

Time development of (a) $⟨\widehat{N}⟩$ and (b) $(\mathrm{\Delta }\widehat{u}{)}^2+(\mathrm{\Delta }\widehat{v}{)}^2$ for the initial coherent states $\mid 10,-10⟩$ in terms of normalized time $gt$ for different values of $D∕\Gamma$. All the other parameters are the same as in Fig. 2.

Figure 4

Time development of (a) $⟨\widehat{N}⟩$ and (b) $(\mathrm{\Delta }\widehat{u}{)}^2+(\mathrm{\Delta }\widehat{v}{)}^2$ for the initial vacuum states and coherent states $\mid 1,-1⟩$, $\mid 2,-2⟩$, and $\mid 3,-3⟩$ for $D∕\Gamma =0.01$. All the other parameters are the same as in Fig. 2.